In a Frenzy, Math Enters Age of Electronic Mail

By GINA KOLATA

Published: June 26, 1990

IN what can only be described as a feeding frenzy, a mathematical advance went from promising concept to completed result in a matter of weeks through an informal worldwide competition conducted by electronic mail.

While the result was exciting, researchers said its true importance lay in the way it was reached.

''I have never seen anything like this,'' said Dr. Ronald Rivest, a mathematician and computer scientist at the Massachusetts Institute of Technology who watched from the sidelines as the research rush went on. ''Computer networks are replacing professional journals and conferences.''

The new electronic mail competition will be likely in many other fields as well because physicists and biochemists, for example, are also increasingly hooked up to computer networks, said Dr. Fan Chung, a research mathematician who is division manager of mathematics, operations research and information science at Bell Communications Research in Morristown, N.J.

Investigators say they have mixed feelings about the predicted onslaught of rapid-fire results from computer network competitions. Many suggest the networks will increase collaboration on difficult problems, generate excitement and result in faster solution of problems.

But Dr. Laszlo Babai of the University of Chicago, who participated in the recent competition, said that proofs by electronic mail place some researchers at a disadvantage. He said scientists in Eastern Europe, third world countries and even much of Japan are not hooked up electronically the way those in the United States, Western Europe and Israel are.

In addition, Dr. Babai added, researchers who help the work on its way but do not get the final answer can feel deprived of the credit they would have got if the work had proceeded at a more measured pace. ''All the credit goes to the one who did the last step,'' Dr. Babai said.

The race began on Nov. 27 when Dr. Noam Nisan, a postdoctoral student at the Massachusetts Institute of Technology, got an idea that could overturn mathematicians' ideas of how difficult certain problems are. Researchers have been stymied by a series of practical problems that sound simple but that seem to be so difficult to solve that they are almost beyond comprehension. Their solutions require so many computations that they make seemingly large numbers, like the number of atoms in the universe, look trivial. So mathematicians and computer scientists have looked for ways to determine whether a problem is going to be impossible to solve.

When asked for an example of a difficult problem, mathematicians invariably trot out the one they call the Traveling Salesman. A salesman has to find a route that takes him through a group of cities. What is the shortest possible distance he must travel to visit each city once? It sounds easy and it is important. The routing of telephone lines, for example, is a traveling salesman problem. But it turns out that the only way that anyone knows to get a general answer to such a problem is to try every route.

Checking a Million Billion Routes

Dr. Chung has calculated that if a computer can check a million billion routes every second, and if the computer started cranking away at the beginning of the universe, it would have taken until 1990 to check all the possible routes for a tour of 33 cities.

When problems get to be that hard, mathematicians have had trouble categorizing them in classes according to how difficult they really would be to solve. They had devised a classification scheme, but the scheme was difficult to verify.

But Dr. Nisan, inspired by recent related discoveries by Dr. Richard Lipton of Princeton University, Dr. Joan Feigenbaum of A.T.&T. Bell Laboratories and a Harvard University graduate student, Donald Beaver, suggested that it might be possible to use a probabilistic proving system, where a fact can almost be verified - but not to absolute certainty - to collapse some of the previous classifications.

''This went against all previous intuition,'' Dr. Babi said, and it caused enormous excitement among researchers. If Dr. Nisan's idea was correct, it could mean that some of these problems were not as hard as they had been thought to be.

Idea Is Sent Out Worldwide

Dr. Nisan says he sent his idea out to about 10 friends by computer mail, and then went home to Jerusalem, where he had accepted a position on the faculty at Hebrew University. Almost immediately afterward, he left for Brazil on a vacation.

While Dr. Nisan was away, mathematicians around the world distributed his idea to each other and began working on it at a frenzied race. Seventeen days later, Dr. Carsten Lund, Dr. Lance Fortnow and Dr. Howard Karloff of the University of Chicago sent out the next leap forward on electronic mail and their result was copied and recopied by computers around the world. Thirteen days later, Dr. Adi Shamir, a mathematician at the Weizmann Institute of Science in Rehovot, Israel, hit the jackpot, announcing, once again, through electronic mail, that Dr. Nisan's original idea was correct and that he could prove it. Finally, 22 days later, the University of Chicago group, including Dr. Babai, put the final touches on the result.

Last Wednesday, again by electronic mail, the competing groups got notice that five papers on the result had been accepted for a highly selective scientific meeting to be held next October.

Dr. Chung said, ''If Noam Nisan did not put his stuff on the network, if he had just worked on it by himself, it is the opinion of everyone that he should have been able to figure out the whole thing.''

But Dr. Nisan said that he was not concerned that he had been left out of the race. ''I've heard some people say I should have kept the idea a secret,'' he said. ''But it's supposed to be a compliment when people work on your ideas. I thought it was very nice and I don't think bad things will happen to my career.''